Mesoscopic interparticle potentials in the lattice Boltzmann equation for multiphase fluids

Hybrid lattice-Boltzmann-finite-difference approach for the simulation of micro-phase-change-material slurry in convective flow

In this paper, we present a hybrid numerical scheme that couples the lattice Boltzmann method (LBM) with the finite difference method (FDM) to model micro-phase-change-material (MPCM) suspensions in a minichannel. Within this framework, the LBM was employed to solve the continuity, momentum, and energy equations for the fluid domain, while a Lagrangian scheme replicates the motion of MPCM particles. The LBM is coupled with an FDM solver which operates under the lumped capacitance assumption to address the phase-change phenomena within the microparticles. This hybrid coupling eliminates the necessity for any specific treatment in handling phase transitions and tracking phase interfaces. The proposed method is first evaluated on classic particle cases, demonstrating its ability to achieve four-way coupling. Furthermore, the current model effectively adapted viscosity changes when integrating the microparticles, obviating the need for homogenous viscosity models. Subsequently, the potential of this approach is demonstrated by examining the influence of the near-wall thermal interaction of MPCM particles considering three scenarios based on particle density: light (ρ_{p}<ρ_{f}), neutrally buoyant (ρ_{p}≈ρ_{f}), and dense (ρ_{p}>ρ_{f}) microparticles. The hybrid approach further revealed insights into the impact of the volume fraction on the heat transfer coefficient as well as on the overall heat transfer coefficient and performance index from a Lagrangian perspective.

Mesoscale modelling of miscible and immiscible multicomponent fluids

A mesoscopic simulation method based on the integration of dissipative particle dynamics (DPD), smoothed particle hydrodynamics (SPH) and computational thermodynamics (CT) has been developed. The kinetic behaviours of miscible and immiscible fluids were investigated. The interaction force between multicomponent mesoscopic particles is derived from the system free energy. The diffusivity of the components in non-ideal solution is determined by the chemical potential. The proposed method provides convincing predictions to the effects of convection, diffusion and microscopic interaction on the non-equilibrium evolution of engineering fluids, and demonstrates a potential to simulate more complicated phenomena in materials processing.

Assessment of interaction potential in simulating nonisothermal multiphase systems by means of lattice Boltzmann modeling

The pseudopotential lattice Boltzmann model (PP-LBM) is a very popular model for simulating multiphase systems. In this model, phase separation occurs via a short-range attraction between different phases when the interaction potential term is properly chosen. Therefore, the potential term is expected to play a significant role in the model and to affect the accuracy and the stability of the computations. The original PP-LBM suffers from some drawbacks such as being capable of dealing with low density ratios only, thermodynamic inconsistency, and spurious velocities. In this paper, we aim to analyze the PP-LBM with the view to simulate single-component (non-)isothermal multiphase systems at large density ratios and in spite of the presence of spurious velocities. For this purpose, the performance of two popular potential terms and of various implementation schemes for these potential terms is examined. Furthermore, the effects of different parameters (i.e., equation of state, viscosity, etc.) on the simulations are evaluated, and, finally, recommendations for a proper simulation of (non-)isothermal multiphase systems are presented.

Thermodynamically Constrained Averaging Theory Approach for Modeling Flow and Transport Phenomena in Porous Medium Systems: 8. Interface and Common Curve Dynamics

This work is the eighth in a series that develops the fundamental aspects of the thermodynamically constrained averaging theory (TCAT) that allows for a systematic increase in the scale at which multiphase transport phenomena is modeled in porous medium systems. In these systems, the explicit locations of interfaces between phases and common curves, where three or more interfaces meet, are not considered at scales above the microscale. Rather, the densities of these quantities arise as areas per volume or length per volume. Modeling of the dynamics of these measures is an important challenge for robust models of flow and transport phenomena in porous medium systems, as the extent of these regions can have important implications for mass, momentum, and energy transport between and among phases, and formulation of a capillary pressure relation with minimal hysteresis. These densities do not exist at the microscale, where the interfaces and common curves correspond to particular locations. Therefore, it is necessary for a well-developed macroscale theory to provide evolution equations that describe the dynamics of interface and common curve densities. Here we point out the challenges and pitfalls in producing such evolution equations, develop a set of such equations based on averaging theorems, and identify the terms that require particular attention in experimental and computational efforts to parameterize the equations. We use the evolution equations developed to specify a closed two-fluid-phase flow model.

Lattice Boltzmann method for Lennard-Jones fluids based on the gradient theory of interfaces

In the present study we propose a lattice Boltzmann equation (LBE) model derived from density gradient expansions of the discrete BBGKY evolution equations. The model is based on the mechanical approach of the gradient theory of interfaces. The basic input is the radial distribution function, which is related exclusively to the molecular interaction potential, rather than semiempirical equations of state used in previous LBE models. This function can be provided from independent molecular simulations or from approximate theories. Evidently the accuracy of the interaction potential, and thus the radial distribution function, reflects on the accuracy of the thermodynamic properties and consistency of the derived LBE model. We have applied the proposed model to obtain equilibrium bulk and interfacial properties of a Lennard-Jones fluid at different temperatures, T, close to critical, T(c). The results demonstrate that the LBE model is in excellent agreement with gradient theory as well as with independent literature results based on different molecular simulation approaches. Hence the proposed LBE model can recover accurately bulk and interfacial thermodynamics for a Lennard Jones fluid at T/T(c)>0.9.

Thermodynamic consistency of liquid-gas lattice Boltzmann methods: interfacial property issues

In the present study we examine the thermodynamic consistency of lattice Boltzmann equation (LBE) models that are based on the forcing method by comparing different numerical treatments of the LBE for van der Waals fluids. The different models are applied for the calculation of bulk and interfacial thermodynamic properties at various temperatures. The effect of the interface density gradient parameter, kappa , that controls surface tension, is related explicitly with the fluid characteristics, including temperature, molecular diameter, and lattice spacing, through the employment of a proper intermolecular interaction potential. A comprehensive analysis of the interfacial properties reveals some important shortcomings of the LBE methods when central finite difference schemes are employed in the directional derivative calculations and proposes a proper treatment that ensures thermodynamically consistent interfacial properties in accord with the van der Waals theory. The results are found to be in excellent quantitative agreement with exact results of the van der Waals theory preserving all the major features of the interfacial characteristics of vapor-liquid systems of different shapes and sizes.

Bubble formation in lattice Boltzmann immiscible shear flow

Bubble formation and the effect of shear on bubble formation in a van der Waals fluid is investigated by means of lattice Boltzmann mesoscale simulations. In the absence of shear, the maximum number of formed bubbles increases with undercooling but the incubation time before bubble formation decreases dramatically. The results are in agreement with classical phase transition theory. In shear flow, the maximum number of bubbles is not affected by shear but the bubble growth rate is accelerated. The effect of shear on bubble growth rate weakens at large undercoolings. The reasons are twofold. On the one hand the highly undercooled system takes less time to complete phase transition due to the large driving force so that there is less time to accumulate the flow effect. On the other hand the mechanism for bubble growth changes from coarsening to coalescence at large undercoolings.